% function [Ki,K,Kd] = area2PID_dist (A0,A1,A2,A3,A4,A5,Kmax);
%
% Function araa2PID_dist calculates parameters of the PID controller:
%
% u = (Ki/s + K + Kd*s) * e
%
% from the measured areas of the process A0 to A5 (A0 is the process steady-state gain)
% for "optimal" disturbance rejection.
% The parameter Kmax represents the highest allowed open-loop gain K*A0 

function [Ki,K,Kd] = area2PID_dist (A0,A1,A2,A3,A4,A5,Kmax);

[Ki,K,Kd] = area2PID (A0,A1,A2,A3,A4,A5,Kmax);
D = (2*A0*A1*A2*Kd + A2^2 - A1*A3 - A0^2*A3*Kd-Kd*A1^3)*(A1+A0^2*Kd)^2;
if (D < 0)
   D = 0;
end;
K = (A0*A3 - A0*A1^2*Kd - A1*A2 + A0^2*A2*Kd + sqrt(D))/(2*A0*A1*A2 - A1^3 - A0^2*A3);

Tmp = K*A0;							% Nominal gain

if (Tmp > Kmax)
   K = Kmax/A0;
end;

if (Tmp < 0)
   K = 0;
end;

Ki = 0.5*(1 + 2*A0*K + A0^2*K^2)/(A1 + A0^2*Kd);
if (Ki*A0 < 0)
   Ki = 0;
end;